What causes the wolf fifth in meantone temperament?

In meantone temperament, the "wolf" fifth is not caused by a single, isolated error, but rather by the system's inherent limitation in accommodating keys beyond its designed range.12

To achieve pure major thirds, meantone tuning flattens the fifths by a quarter of a comma. Because the keyboard provides only 12 fixed notes per octave, this tuning scheme can only support a limited number of keys (typically those using three sharps and two flats). When a composition requires an enharmonic note outside of this established set—such as needing a $D♯$ when only an $E♭$ is available—the resulting interval between the available notes becomes severely out of tune.12

This specific, highly dissonant interval, such as the $G♯$–$E♭$ fifth, is nearly two commas out of tune and produces a harsh, beating sound known as the "wolf". This limitation eventually led to the adoption of equal temperament, which distributes tuning imperfections evenly across all keys to allow for greater harmonic flexibility.21